Investigating the effect of bio-convection, chemical reaction, and motile microorganisms on Prandtl hybrid nanofluid flow across a stretching sheet

Due to extensive application in extruding plastic sheet processes, liquid film condensation, glass blowing, biopolymer cylinder coatings, paper manufacture, and other processes, the thermodynamical characteristics of non-Newtonian fluids across stretched surfaces have acquired ubiquitous essence. Therefore, the present communication aims to openly elucidate Prandtl fluid flow characteristics produced by a stretching surface. In this analysis, a hybrid nanofluid (HNF) is considered by using pure water as a base fluid and two various nanomaterials (copper and Titanium dioxide) as nanoparticles in the characterization of heat transfer. Moreover, the goal of this investigation is to ascertain the heat transfer characteristics of a magnetohydrodynamic (MHD) Prandtl hybrid nanofluid (PHNF) model. Across the stretching sheet, this article interrogates the inclined MHD, chemical reaction, bio-convection, linearly thermal radiation, and Darcy-Forchheimer (DF) effect in the attendance of porous medium of HNF. The modified Buongiorno model for nanofluids is adopted to explore heat transport augmentation. It includes the mechanics of nanoparticle random motion and thermo-migration as well as useful nanofluid characteristics. Additionally, the outcomes are contrasted with nanofluid flow. With the right level of similarity, the process converts partial differential equations emerging in nanofluidic systems into nonlinear differential equation systems. The (FDM) finite difference approach (Lobatto IIIA) is used for the nonlinear nanofluid issue with the precision of order 4 to 5 and is implemented using a variety of collocation locations. The strength of (Lobatto IIIA) is its effectiveness in handling coupled differential equations that are extremely nonlinear. The higher-order differential equations are converted into a first-order method utilizing the boundary value dilemma (bvp4c) solver, which is part of the MATLAB software package, to computationally analyze the simplified mathematical model. The data obtained demonstrated a high degree of accuracy and symmetry when measured against previously published studies. Following earlier studies, increasing the values of the Prandtl parameters increases the velocity profiles of both basic nanofluid and HNF, while the Forchheimer and porosity parameters reduce fluid velocity. Additionally, as the values of the magnetic parameters increase, the temperature and concentration of simple and HNFs rise as well.